{"id":"https://openalex.org/W2026013585","doi":"https://doi.org/10.1109/ifsa-nafips.2013.6608393","title":"Partial orders on the truth value algebra of finite type-2 fuzzy sets","display_name":"Partial orders on the truth value algebra of finite type-2 fuzzy sets","publication_year":2013,"publication_date":"2013-06-01","ids":{"openalex":"https://openalex.org/W2026013585","doi":"https://doi.org/10.1109/ifsa-nafips.2013.6608393","mag":"2026013585"},"language":"en","primary_location":{"id":"doi:10.1109/ifsa-nafips.2013.6608393","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ifsa-nafips.2013.6608393","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034730206","display_name":"John Harding","orcid":"https://orcid.org/0000-0002-8539-0372"},"institutions":[{"id":"https://openalex.org/I10052268","display_name":"New Mexico State University","ror":"https://ror.org/00hpz7z43","country_code":"US","type":"education","lineage":["https://openalex.org/I10052268"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John Harding","raw_affiliation_strings":["Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, USA","Dept. of Math. Sci., New Mexico State Univ., Las Cruces, NM, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, USA","institution_ids":["https://openalex.org/I10052268"]},{"raw_affiliation_string":"Dept. of Math. Sci., New Mexico State Univ., Las Cruces, NM, USA","institution_ids":["https://openalex.org/I10052268"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110609480","display_name":"Carol L. Walker","orcid":null},"institutions":[{"id":"https://openalex.org/I10052268","display_name":"New Mexico State University","ror":"https://ror.org/00hpz7z43","country_code":"US","type":"education","lineage":["https://openalex.org/I10052268"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Carol Walker","raw_affiliation_strings":["Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, USA","Dept. of Math. Sci., New Mexico State Univ., Las Cruces, NM, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, USA","institution_ids":["https://openalex.org/I10052268"]},{"raw_affiliation_string":"Dept. of Math. Sci., New Mexico State Univ., Las Cruces, NM, USA","institution_ids":["https://openalex.org/I10052268"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109977624","display_name":"Elbert A. Walker","orcid":null},"institutions":[{"id":"https://openalex.org/I10052268","display_name":"New Mexico State University","ror":"https://ror.org/00hpz7z43","country_code":"US","type":"education","lineage":["https://openalex.org/I10052268"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Elbert Walker","raw_affiliation_strings":["Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, USA","Dept. of Math. Sci., New Mexico State Univ., Las Cruces, NM, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, USA","institution_ids":["https://openalex.org/I10052268"]},{"raw_affiliation_string":"Dept. of Math. Sci., New Mexico State Univ., Las Cruces, NM, USA","institution_ids":["https://openalex.org/I10052268"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I10052268"],"apc_list":null,"apc_paid":null,"fwci":0.2288,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.46894656,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"163","last_page":"168"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9901999831199646,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9767000079154968,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7206951379776001},{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.5805454850196838},{"id":"https://openalex.org/keywords/binary-operation","display_name":"Binary operation","score":0.49496978521347046},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.4906700849533081},{"id":"https://openalex.org/keywords/complete-lattice","display_name":"Complete lattice","score":0.46960386633872986},{"id":"https://openalex.org/keywords/unit-interval","display_name":"Unit interval","score":0.46593111753463745},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4594131410121918},{"id":"https://openalex.org/keywords/idempotence","display_name":"Idempotence","score":0.4309236407279968},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4135086238384247},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.38170021772384644},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34804850816726685},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30642491579055786}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7206951379776001},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.5805454850196838},{"id":"https://openalex.org/C185529760","wikidata":"https://www.wikidata.org/wiki/Q164307","display_name":"Binary operation","level":2,"score":0.49496978521347046},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.4906700849533081},{"id":"https://openalex.org/C201640847","wikidata":"https://www.wikidata.org/wiki/Q2362924","display_name":"Complete lattice","level":3,"score":0.46960386633872986},{"id":"https://openalex.org/C128394911","wikidata":"https://www.wikidata.org/wiki/Q1987578","display_name":"Unit interval","level":2,"score":0.46593111753463745},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4594131410121918},{"id":"https://openalex.org/C172252984","wikidata":"https://www.wikidata.org/wiki/Q368988","display_name":"Idempotence","level":2,"score":0.4309236407279968},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4135086238384247},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38170021772384644},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34804850816726685},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30642491579055786},{"id":"https://openalex.org/C183992945","wikidata":"https://www.wikidata.org/wiki/Q2495574","display_name":"Universality (dynamical systems)","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ifsa-nafips.2013.6608393","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ifsa-nafips.2013.6608393","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1998805535","https://openalex.org/W2026457244","https://openalex.org/W2036086407","https://openalex.org/W2053128243","https://openalex.org/W2056310122","https://openalex.org/W2057266079","https://openalex.org/W2063041878","https://openalex.org/W2069693518","https://openalex.org/W2088220507","https://openalex.org/W2102616948","https://openalex.org/W2103729992","https://openalex.org/W2147340301","https://openalex.org/W2598771954","https://openalex.org/W3188118795","https://openalex.org/W4237535572","https://openalex.org/W4254730433","https://openalex.org/W6836461034"],"related_works":["https://openalex.org/W1547667760","https://openalex.org/W4291944364","https://openalex.org/W2951492630","https://openalex.org/W2322615891","https://openalex.org/W4238189986","https://openalex.org/W3116819432","https://openalex.org/W4236037843","https://openalex.org/W1993276116","https://openalex.org/W3025765140","https://openalex.org/W1981153708"],"abstract_inverted_index":{"The":[0],"elements":[1],"of":[2,7,14,26,46,105,140,162],"the":[3,15,27,47,98,103,113,125,131,138,152,156],"truth":[4],"value":[5],"algebra":[6,31,157],"type-2":[8],"fuzzy":[9],"sets":[10],"are":[11,60,65,118,122],"all":[12],"mappings":[13],"unit":[16,48],"interval":[17,49],"into":[18],"itself,":[19],"with":[20,97,142],"operations":[21,56,63],"given":[22,101,144],"by":[23,50,102],"various":[24,38],"convolutions":[25],"pointwise":[28],"operations.":[29],"This":[30],"can":[32],"be":[33],"specialized":[34],"and":[35,54,68,70,136],"generalized":[36],"in":[37,164],"interesting":[39],"ways.":[40],"Here":[41,77],"we":[42,78,111],"replace":[43],"each":[44,72,89],"copy":[45],"a":[51,74,91,143,149,165],"finite":[52],"chain,":[53],"define":[55],"analogously.":[57],"Among":[58],"these":[59,80,106],"two":[61,107,120],"binary":[62],"which":[64,110],"idempotent,":[66],"commutative,":[67],"associative,":[69],"thus":[71],"yields":[73],"partial":[75,81,99,108],"order.":[76,115,154],"investigate":[79],"orders.":[82],"It":[83],"is":[84,90,96,148,159],"easy":[85],"to":[86],"show":[87],"that":[88,119,137],"lattice.":[92],"One":[93],"principal":[94],"concern":[95],"order":[100,127],"intersection":[104],"orders,":[109],"call":[112],"double":[114,126,153],"Some":[116],"results":[117],"functions":[121,141],"incomparable":[123],"under":[124,151],"unless":[128],"they":[129],"have":[130],"same":[132],"least":[133,145],"upper":[134,146],"bound,":[135],"set":[139],"bound":[147],"lattice":[150],"Thus":[155],"itself":[158],"an":[160],"antichain":[161],"lattices":[163],"natural":[166],"way.":[167]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}